Full text of DOI:10.1111/j.1151-2916.2003.tb03390.x

J. Am. Ceram. Soc., 86 [5] 870–72 (2003)
journal
Grain Boundary Grooving Studies of
Yttrium Aluminum Garnet (YAG) Bicrystals
M. I. Peters† and I. E. Reimanis*
Metallurgical and Materials Engineering Department, Colorado School of Mines, Golden, Colorado 80401
Grain boundary grooving experiments were conducted with
⌺5 (210) twist boundaries in Y3Al5O12 (YAG) with the goal of
extracting information on diffusion in YAG. Planar bound-
aries oriented 90° to the surface were annealed in air at various
times and temperatures. Atomic force microscopy was used to
characterize the subsequent grooves. The Mullins approach
leads to the following expression for the diffusion coefficient:
D (m2/s) ؍ 3.9 ؋ 10؊10 exp[؊330 ؎ 75 (kJ/mol)/RT]. The
relatively low activation energy agrees well with earlier oxygen
tracer diffusion measurements on YAG, suggesting that oxy-
gen is the limiting diffusing species in boundary grooving of
YAG.
activation energies calculated are compared with those reported in the
literature.
II. Experimental Procedure
⌺5 (210)/[001] twist boundaries in Y3Al5O12 were formed by
bonding two single crystals of YAG. The bonding procedure is
briefly described here. Details may be found elsewhere.7,8 High-
purity (undoped) YAG single crystals grown along the [111] axis
were sectioned to dimensions 25 mm in diameter and 25 mm in
height, and polished on [210] faces to within 0.1° of the [210]
plane. These crystal orientations were chosen as part of a study on
the grain boundary structure in YAG.9 The surfaces were sputter
cleaned and bonded at 1550°C for 6 h under an applied stress of 5
MPa in an ultra-high-vacuum bonding machine (vacuum level
Ͻ7 ϫ 10Ϫ8 torr at maximum temperature) at Lawrence Livermore
National Laboratory.9 Grain boundary grooving specimens ϳ4
mm ϫ 5 mm ϫ 6 mm were subsequently sectioned from the
bonded crystals using an Isomet slow speed diamond saw. The
boundary plane intersected the surface at 90° as shown in Fig. 1.
Crystals on both sides of the boundary had the same crystallo-
graphic orientation, and as a result, most of the observed groove
profiles were symmetric, though some boundaries that were
annealed for longer times exhibited groove asymmetry and even
some grain boundary migration.8 The surfaces on which grain
boundary grooving measurements were made were polished with
successively smaller diamond particle media, until the final polish
with 0.1 ␮m diamond was completed. Samples were scanned with
an atomic force microscope to quantify the surface roughness
before heating.
Five different bicrystal specimens were heated at ϳ10°C/min to
1550°, 1587°, 1623°, 1663°, and 1700°C for 30 to 150 min in an
air furnace with MoSi2 heating elements. The cooling rate was
ϳ10°C/min from elevated temperatures to about 1000°C, at which
temperature the rate became slower. The soak time for the two
specimens heat-treated at the highest temperatures was shorter
because at longer times, the geometry of the boundary became
asymmetrical, invalidating the Mullins approach. A sixth specimen
was heated at 1600°C for 2.5 h, cooled, then subsequently heated
for an additional 5 and 10 h. The purpose of this sixth specimen
was to use the relationship between the groove growth and the time
to establish the mechanism of diffusion. As discussed below,
Mullins’ analysis predicts different relationships for volume dif-
fusion, surface diffusion, and evaporation–condensation mecha-
nisms.7 After heating, there was no visible contamination (e.g.,
with silica from MoSi2 elements) on the YAG surfaces, but a
detailed inspection was not made. On each specimen, eight atomic
force microscopy area scans were performed along the length of
the boundary using a multimode atomic force microscopy scanner
(Digital Instruments, Santa Barbara, CA). Each area scan was
sectioned 10 times at different locations along the boundary to
produce an average of 80 scans for each temperature. From each of
these scans, an average peak-to-peak distance of the grain bound-
ary groove was recorded.
I. Introduction
TTRIUM ALUMINUM GARNET (YAG) has potential elevated temper-
Y
ature structural applications because of its high creep resistance
and low susceptibility to degradation in oxidative environments.1,2 As
with most oxides, diffusional creep is expected to be an important
deformation mechanism, particularly for polycrystalline YAG, since
the large Burgers vector (10.4 Å, b ϭ 21[111]) provides a considerable
barrier for dislocation motion. There have been a limited number of
creep studies on single-crystal YAG,1–3 and only one on polycrystal-
line YAG.4 A value of nearly unity for the stress exponent in the latter
study suggests that polycrystalline YAG creeps principally by a
diffusional mechanism, similar to other oxides. The reported activa-
tion energy for creep of polycrystalline YAG is 584 kJ/mol,4 while
those for single-crystal YAG tested at relatively low strain rates vary
between 596 and 720 kJ/mol.1–3 The fact that the activation energies
for the single-crystal studies are similar to that for the polycrystalline
study indicates that diffusion probably dominates mass transport
during creep in single-crystal YAG. Further, as pointed out by
Parthasarathy et al. ,4 the fact that these activation energies are much
higher than the activation energy (297–325 kJ/mol) for the volume
diffusion of oxygen in YAG, as measured by tracer methods,5 it
seems likely that the cations rather than oxygen control diffusional
creep in YAG. Indeed, a recent study concludes that the activation
energy for lattice and grain boundary diffusion of the Yb cation YAG
is approximately 550 kJ/mol.6 The present study uses the indirect
technique of grain boundary grooving to evaluate the diffusion
coefficient of YAG. In this technique, the geometrical changes in
YAG grain boundaries exposed to high temperature are measured.
Subsequently, Mullins’ theory of grain boundary grooving7 is applied
to describe the changes and back-calculate a diffusion coefficient. The
R. S. Hay—contributing editor
Manuscript No. 186713. Received August 23, 2002; approved October 29, 2002.
This work was supported by the Los Alamos National Laboratory through the U.S.
Department of Energy, Office of Basic Energy Sciences.
*Member, American Ceramic Society.
†Present address: Los Alamos National Laboratory, Los Alamos, NM 87545.
870

May 2003
Communications of the American Ceramic Society
871
Fig. 1. YAG bicrystal specimen (boundary not visible) with schematic
showing the boundary orientation relative to the surface.
III. Results
Fig. 3. Groove peak-to-peak distance, W, plotted as a function of time, t,
for YAG heat-treated at 1600°C.
Figure 2 illustrates a typical groove geometry formed after a
heat treatment of 1600°C for 2 h. As may be seen, the groove
shape is symmetrical. The groove peak-to-peak distance, W, is
plotted as a function of time on a logarithmic scale for the sample
exposed three times at 1600°C in Fig. 3. These data reveal a power
exponent equal to 0.346 Ϯ 0.045, very close to 1/3 that is predicted
when a volume diffusion mechanism dominates the groove evo-
lution. In comparison, the predicted power exponent for surface
diffusion is 1/4. Based on this, it was assumed that volume
diffusion controls most of the mass transport at the grain boundary
groove.
an activation energy of 330 kJ/mol (Ϯ75 kJ/mol). Accordingly, the
diffusion can be expressed as
D(Y Al O )ϭ 3.9 ϫ 10Ϫ10 exp͓Ϫ330 Ϯ 75 ͑kJ/mol͒/RT͔
(3)
3
5 12
Diffusion coefficients were calculated using10
IV. Discussion
1/3
The relatively small diffusion coefficients and high activation
energy measured here are commensurate with the observation that
polycrystalline YAG is extremely creep resistant compared with
other oxides. There exists very limited information concerning
mass transport in YAG. Besides the oxygen tracer diffusion
measurements of Haneda et al.,5 and the direct measurements of
Yb diffusion by Jime´nez-Melando et al.,6 the only other measure-
ments of mass transport in YAG are from creep experiments.1–4 If
one assumes that diffusion controls creep in these latter studies,
then the measured activation energies should be the same as those
for diffusion. These creep activation energies for the creep of
single-crystal and polycrystalline YAG vary between 550 and 720
kJ/mol.1–4 In comparison, that measured here for grain boundary
grooving is much lower: 330 Ϯ 75 kJ/mol. The difference suggests
that the diffusional process that controls grain boundary grooving
is different from that controlling creep in YAG. Because the
activation energy measured here is nearly equivalent to that
measured for oxygen diffusion in YAG (297–325 kJ/mol),5 it is
inferred that oxygen diffusion limits atomic transport in grain
boundary grooving. In contrast, as suggested by Parthasarathy et
al.,4 it must be that cation diffusion limits atomic transport in
creep. If it is assumed that volume diffusion operates in both bulk
creep and grain boundary grooving, then it must be that the
presence of the free surface alters the diffusion process. Specifi-
cally, if cations diffuse rapidly along the free surface, then oxygen
diffusion through the bulk would be rate limiting.
W ϭ ͑ AЈt͒
(1)
where W is the peak-to-peak distance on the groove, t is time, and
AЈ is given by
AЈ ϭ 125n⍀2D␥v/kT
(2)
n is the number of atoms per unit volume (n ϭ 9.23 ϫ 1022
atoms/cm3), ⍀ is the atomic volume (⍀ ϭ 1.73 ϫ 10Ϫ21 cm3),11
D is the volume diffusion coefficient, ␥v is the surface energy of
YAG, k is Boltzmann’s constant, and T is the temperature. Because
the value for the surface energy of YAG is not known, the
calculated value for Al2O3 at 1650°C (␥v ϭ 2500 erg/cm2)11 was
used. This approximation influences the accuracy of the calculated
diffusion coefficient, but not the activation energies. Table I
summarizes the results and Fig. 4 plots the diffusion coefficient as
a function of inverse temperature.
Repeated measurements at fixed temperatures of grain bound-
ary grooves revealed no more than a 15% error in the diffusion
coefficient values. The error bars in Fig. 4 represent this error. A
best linear fit is shown in Fig. 4. The slope of this linear fit reveals
Table I. Diffusion Coefficients at Various Temperatures
Temperature
Heat treatment
time (min)
W (Ϯ5%)
Diffusion coefficient
(°C)
(nm)†
(Ϯ15%) (cm2/s)
1550
1587
1625
1663
1700
150
150
150
60
1040
835
9.1 ϫ 10Ϫ15
4.7 ϫ 10Ϫ15
74 ϫ 10Ϫ15
2.3 ϫ 10Ϫ14
3.8 ϫ 10Ϫ14
957
1020
957
30
Fig. 2. Typical grain boundary groove, measured by atomic force
microscopy. Note the symmetrical shape of the boundary.
†Average “peak-to-peak” distance.

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Vol. 86, No. 5
Only a direct technique of measuring diffusion, such as a tracer
method will establish whether oxygen or cations control diffusion
for the different geometrical situations discussed above. Until
those measurements are performed, indirect methods such as grain
boundary grooving provide insights into possible diffusional
mechanisms. In the present case, the experimental observations,
when considered in conjunction with the earlier deduction that
cations control diffusional creep in YAG4 lead to the conclusion
that cations diffuse more rapidly on the surface than in the bulk. It
seems difficult to ignore this deduction since the cations in YAG
are large ions and since it is fairly well established that cations
control diffusion in other oxides. It is not immediately obvious
why cation diffusion might be more rapid on the surface. Nor is it
clear why oxygen diffusion would not also be correspondingly
more rapid. Further studies on diffusion in YAG should be directed
at establishing diffusional mechanisms for bulk, grain boundaries
and surfaces.
V. Conclusions
Fig. 4. Diffusion coefficients of YAG as a function of temperature
calculated from grain boundary groove measurements.
Grain boundary grooving studies have been used to extract
information on diffusion in YAG. An application of Mullins’
theory of grooving shows that volume diffusion controls mass
transport during grain boundary grooving. The diffusion coeffi-
cients at various times and temperatures were calculated, based on
the geometric changes in the groove. The surface energy of Al2O3
was used in the calculation, introducing an error in the diffusion
coefficients. However, the activation energy calculated is not
affected. The activation energy determined was comparable to that
measured for oxygen diffusion in YAG, implying that diffusion
during grain boundary grooving is limited by oxygen diffusion.
Another explanation for the difference between reported acti-
vation energies for creep and grain boundary grooving in YAG
concerns the applicability of the Mullins analysis to the experi-
mental conditions used here. In particular, it is possible that an
evaporation/condensation or a surface diffusion mechanism oper-
ates during grain boundary grooving. Two comments in this regard
are made. First, it is unlikely that an evaporation/condensation
mechanism dominates the grooving, since the resulting boundaries
would have very different profiles from those observed here. In
evaporation/condensation the grain boundary region forms a
groove, but there are no protrusions formed higher than the
original surface, as is the case for surface and volume controlled
diffusion. Second, if it is assumed that surface diffusion dominates
grain boundary grooving, an application of Mullins’ analysis leads
to an activation energy on the order of 300 kJ/mol, on the same
order as that found for volume diffusion. Thus, in the case where
surface diffusion dominates, it would also be concluded that
oxygen diffusion is rate limiting during grain boundary grooving.
It is finally pointed out that the conclusions reported here
depend on the 1/3 width versus time exponent reported in Fig. 3.
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If this value is in error, and if surface diffusion dominates the
1
grooving process (see the slope
⁄4 line in Fig. 3), then the
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